IS–LM to AD–AS · Lesson 7 of 10
The Phillips curve as aggregate supply
Lesson 6 described supply as a curve in output and the price level. Rewrite it in unemployment and inflation and you get the Phillips curve, the most asked single topic in this module. It now has a full course of its own, linked below; this lesson keeps the part that belongs to the AD–AS model: the curve year by year, where the natural rate comes from, and the cost of disinflation.
A question to hold on to
Full-employment output is ₹1 trillion and the natural rate of unemployment is 6%. If actual unemployment is 8%, what, by Okun’s law, is the gap between full-employment output and actual output, in billions of rupees?
IIT JAM 2021Solved at the end ↓
Where the topics went
This lesson has a full course behind it
Lesson 6 gave supply as a curve in output and the price level. Rewrite that curve with unemployment and inflation on the axes and you have the Phillips curve: the short-run aggregate supply curve seen from the labour market. Okun’s law is the bridge between the two pictures, since it turns the output gap into an unemployment gap. The topics that used to be chapters of this page are now lessons of their own, each with its own interactive and past-paper sets:
- Measuring inflation and measuring unemployment: price indices, the labour force, the types of unemployment.
- Causes of inflation and its costs: demand-pull, cost-push and structural inflation, the real rate, who gains and loses, seigniorage.
- The original Phillips curve, Okun’s law and expectations and the vertical long run.
- Where the natural rate comes from, supply shocks and stagflation and bringing inflation down: wage-setting and price-setting, the shift of the curve, and the sacrifice ratio.
Read together they are the module Inflation, unemployment and the Phillips curve. What stays on this page is the part that belongs to the AD–AS model: the curve year by year, where the natural rate comes from, and the cost of bringing inflation down.
The one-line version
Phillips curve: π = πᵉ − β(u − uₙ). Expectations shift it; in the long run πᵉ = π and unemployment is at the natural rate whatever the inflation rate.
Interactive
The Phillips curve, year by year
Hold unemployment below the natural rate and press the button a few times. With anchored expectations, inflation settles; with adaptive expectations, each year’s inflation becomes next year’s expectation and the short-run curve climbs. The DSE 2021 preset is a question from the paper.
πₜ − πₜᵉ = 0.1 − 3uₜ, so β = 3 and uₙ = 0.1/3 = 3.33%. Inflation was 2% and the central bank holds u at 3% for ever.
The Phillips curve this year
Inflation, year by year
Year 1
π = πᵉ − β(u − uₙ) = 2 − 3 × (3 − 3.33) = 3%.
What happens if this goes on
Each year expectations catch up with last year's inflation, the short-run curve shifts up, and inflation rises by β(uₙ − u) = 1 points a year, for as long as u is held there.
IIT JAM 2026 · standard
Expected inflation is 5%, the natural rate 4%, the response to the unemployment gap 0.5, and actual unemployment 5%. What is inflation?
- Apply the curve.π = 5 − 0.5 × (5 − 4) = 4.5.
Answer
4.5%. Unemployment above the natural rate pulls inflation below what was expected.
Interactive
Where the natural rate comes from
Why is the natural rate what it is? Blanchard’s answer, which the Delhi School uses a great deal, puts two relations side by side. Wage-setting: workers bargain for a higher real wage when unemployment is low. Price-setting: firms charge a mark-up m over labour costs, which pins the real wage at A/(1 + m). Only one unemployment rate makes the wage workers claim equal to the wage firms’ prices allow.
Natural rate of unemployment
20%
uₙ = z + m/(1 + m) = 0 + 0.25/1.25. The real wage there is A/(1 + m) = 0.8.
Try the Delhi School’s numbers: a 20% mark-up with W = P(1 − u) gives uₙ = 0.2/1.2 ≈ 17% (DSE 2019); a 25% mark-up gives 20% (DSE 2020). Then move A: the natural rate does not change (DSE 2019).
More monopoly power raises the mark-up, lowers the real wage firms pay and raises the natural rate: output is lower and prices higher, both in the short run and the medium run (UGC NET 2023). Stronger bargaining power or more generous benefits do the same. Efficiency-wage theories (Yellen, Stiglitz and others; UGC NET 2024) explain why firms may pay above the market-clearing wage, to keep workers loyal and productive (DSE 2019), and so why some unemployment persists even in equilibrium. The full treatment, with four wage-setting rules and a workbench, is in Lesson 8 of the inflation module.
From WS–PS to the Phillips curve
Write wage-setting with expected prices, W = Pᵉ·F(u), and price-setting P = (1 + m)W. Then P = Pᵉ(1 + m)F(u): prices exceed expectations when unemployment is low. Put in growth rates, that is the expectations-augmented Phillips curve, and the natural rate is where (1 + m)F(u) = 1. The Delhi School’s questions on this are in Lesson 10.
Policy
The cost of bringing inflation down
To bring inflation down, the central bank must, on this curve, hold unemployment above the natural rate until expectations fall. The lost output per point of inflation removed is the sacrifice ratio. It is larger when wages and prices respond sluggishly to tight money (UGC NET 2025) and smaller when a credible central bank can bring expectations down directly. Output is above potential, a positive output gap, when factors are over-employed (UGC NET 2025). The inflation module prices the cost in Lesson 10, with a lab.
Solving the opening question
The opening question, solved
IIT JAM 2021 · standard
Yf = ₹1 trillion, un = 6%, u = 8%. Find the output gap in billions of rupees.
- Unemployment gap.8 − 6 = 2 points.
- Okun's law with β = 2.Output is 2 × 2 = 4% below potential.
- In rupees.4% of ₹1,000 billion = ₹40 billion.
Answer
40, the key’s answer, which assumes the usual coefficient of 2.
Watch out for
The mistakes examiners are fishing for
- Dividing by the wrong base. Unemployment is a share of the labour force, not the population.
- Frictional against structural. Between jobs is frictional; a skills or industry mismatch is structural.
- Along against shift. A change in actual inflation with expectations fixed moves along the short-run curve; a change in expected inflation or a supply shock shifts it.
- Real rate shortcut. At high rates use (1 + i)/(1 + π) − 1.
- Long-run curve. Monetarists: vertical at un. It is the natural rate, not zero unemployment.
Revise
The lesson on one screen
The lesson on one screen
- Phillips curve
- π = πᵉ − β(u − uₙ): short-run supply seen from the labour market. Expectations shift it; the long run is vertical at uₙ.
- Okun's law
- (Y − Yf)/Yf = −β(u − uₙ), β ≈ 2, links the unemployment gap to the output gap.
- Below uₙ
- Inflation rises year after year (NAIRU: the unemployment rate at which inflation is stable).
- WS–PS
- Real wage A/(1 + m) from price-setting meets wage-setting at uₙ = z + m/(1 + m) in the linear case.
- Disinflation
- Costs output; more with sticky wages and prices, less with credibility.
Practice
Check yourself
Compute
Accelerating inflation
π = πᵉ − 2(u − 5) with πᵉ = last year’s inflation. Inflation is 3% and unemployment is held at 4%. What is inflation after three years?
Quick questions
1If actual unemployment is below the natural rate, we would expect
2In the monetarist view, the long-run Phillips curve is
Real questions
Where the past papers are
The past-paper sets for this topic are in the lessons of the inflation module, each set beside the lesson that teaches it, and the Delhi School’s questions are in Lesson 12.
Read next
All resources →MacroeconomicsIS–LM 8: expectations and the great debatesAdaptive and rational expectations, policy ineffectiveness, the Lucas critique, real business cycles, New Keynesians and business-cycle theories.MacroeconomicsInflation, unemployment and the Phillips curve: a module from price indices to the natural rateA module in twelve lessons: measuring inflation and unemployment, the causes and costs of inflation, the original and expectations-augmented Phillips curves, Okun's law, wage-setting and price-setting, supply shocks, disinflation, the curve in real data, and a lesson of Delhi School problems. With labs, worked questions and graded past papers.MacroeconomicsThe Phillips curve, short run and long runPush unemployment below its natural rate, then watch expectations catch up and pull it back, step by step.